A stochastic parameterization for deep convection based on equilibrium statistics

A stochastic parameterization scheme for deep convection is described, suitable for use in both climate and NWP models. Theoretical arguments and the results of cloud-resolving models, are discussed in order to motivate the form of the scheme. In the deterministic limit, it tends to a spectrum of entraining/detraining plumes and is similar to other current parameterizations. The stochastic variability describes the local fluctuations about a large-scale equilibrium state. Plumes are drawn at random from a probability distribution function (pdf) that defines the chance of finding a plume of given cloud-base mass flux within each model grid box. The normalization of the pdf is given by the ensemble-mean mass flux, and this is computed with a CAPE closure method. The characteristics of each plume produced are determined using an adaptation of the plume model from the Kain-Fritsch parameterization. Initial tests in the single column version of the Unified Model verify that the scheme is effective in producing the desired distributions of convective variability without adversely affecting the mean state.

Evaluation of a bounded high order upwind scheme for 3D incompressible free surface flow computations

fit the context of normalized variable formulation (NVF) of Leonard and total variation diminishing (TVD) constraints of Harten. this paper presents an extension of it previous work by the authors for solving unsteady incompressible flow problems. The main contributions of the paper are threefold. First, it presents the results of the development and implementation of a bounded high order upwind adaptative QUICKEST scheme in the 3D robust code (Freeflow), for the numerical solution of the full incompressible Navier-Stokes equations. Second, it reports numerical simulation results for 1D hock tube problem, 2D impinging jet and 2D/3D broken clam flows. Furthermore, these results are compared with existing analytical and experimental data. And third, it presents the application of the numerical method for solving 3D free surface flow problems. (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved,

A continuously differentiable upwinding scheme for the simulation of fluid flow problems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Evaluation of a bounded high order upwind scheme for 3D incompressible free surface flow computations

fit the context of normalized variable formulation (NVF) of Leonard and total variation diminishing (TVD) constraints of Harten. this paper presents an extension of it previous work by the authors for solving unsteady incompressible flow problems. The main contributions of the paper are threefold. First, it presents the results of the development and implementation of a bounded high order upwind adaptative QUICKEST scheme in the 3D robust code (Freeflow), for the numerical solution of the full incompressible Navier-Stokes equations. Second, it reports numerical simulation results for 1D hock tube problem, 2D impinging jet and 2D/3D broken clam flows. Furthermore, these results are compared with existing analytical and experimental data. and third, it presents the application of the numerical method for solving 3D free surface flow problems. (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved,

Simulation results and applications of an advection bounded scheme to practical flows

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Application of a bounded upwinding scheme to complex fluid dynamics problems

This paper is concerned with an overview of upwinding schemes, and further nonlinear applications of a recently introduced high resolution upwind differencing scheme, namely the ADBQUICKEST [V.G. Ferreira, F.A. Kurokawa, R.A.B. Queiroz, M.K. Kaibara, C.M. Oishi, J.A.Cuminato, A.F. Castelo, M.F. Tomé, S. McKee, assessment of a high-order finite difference upwind scheme for the simulation of convection-diffusion problems, International Journal for Numerical Methods in Fluids 60 (2009) 1-26]. The ADBQUICKEST scheme is a new TVD version of the QUICKEST [B.P. Leonard, A stable and accurate convective modeling procedure based on quadratic upstream interpolation, Computer Methods in Applied Mechanics and Engineering 19 (1979) 59-98] for solving nonlinear balance laws. The scheme is based on the concept of NV and TVD formalisms and satisfies a convective boundedness criterion. The accuracy of the scheme is compared with other popularly used convective upwinding schemes (see, for example, Roe (1985) [19], Van Leer (1974) [18] and Arora & Roe (1997) [17]) for solving nonlinear conservation laws (for example, Buckley-Leverett, shallow water and Euler equations). The ADBQUICKEST scheme is then used to solve six types of fluid flow problems of increasing complexity: namely, 2D aerosol filtration by fibrous filters; axisymmetric flow in a tubular membrane; 2D two-phase flow in a fluidized bed; 2D compressible Orszag-Tang MHD vortex; axisymmetric jet onto a flat surface at low Reynolds number and full 3D incompressible flows involving moving free surfaces. The numerical simulations indicate that this convective upwinding scheme is a good generic alternative for solving complex fluid dynamics problems. © 2012.

Simulation results and applications of an advection bounded scheme to practical flows

This paper reports experiments on the use of a recently introduced advection bounded upwinding scheme, namely TOPUS (Computers & Fluids 57 (2012) 208-224), for flows of practical interest. The numerical results are compared against analytical, numerical and experimental data and show good agreement with them. It is concluded that the TOPUS scheme is a competent, powerful and generic scheme for complex flow phenomena.

A continuously differentiable upwinding scheme for the simulation of fluid flow problems

This paper deals with the numerical solution of complex fluid dynamics problems using a new bounded high resolution upwind scheme (called SDPUS-C1 henceforth), for convection term discretization. The scheme is based on TVD and CBC stability criteria and is implemented in the context of the finite volume/difference methodologies, either into the CLAWPACK software package for compressible flows or in the Freeflow simulation system for incompressible viscous flows. The performance of the proposed upwind non-oscillatory scheme is demonstrated by solving two-dimensional compressible flow problems, such as shock wave propagation and two-dimensional/axisymmetric incompressible moving free surface flows. The numerical results demonstrate that this new cell-interface reconstruction technique works very well in several practical applications. (C) 2012 Elsevier Inc. All rights reserved.

Mixed finite-element methods for elliptic convection-dominated problems arising in semiconductor physics

In this work we develop and analyze an adaptive numerical scheme for simulating a class of macroscopic semiconductor models. At first the numerical modelling of semiconductors is reviewed in order to classify the Energy-Transport models for semiconductors that are later simulated in 2D. In this class of models the flow of charged particles, that are negatively charged electrons and so-called holes, which are quasi-particles of positive charge, as well as their energy distributions are described by a coupled system of nonlinear partial differential equations. A considerable difficulty in simulating these convection-dominated equations is posed by the nonlinear coupling as well as due to the fact that the local phenomena such as "hot electron effects" are only partially assessable through the given data. The primary variables that are used in the simulations are the particle density and the particle energy density. The user of these simulations is mostly interested in the current flow through parts of the domain boundary - the contacts. The numerical method considered here utilizes mixed finite-elements as trial functions for the discrete solution. The continuous discretization of the normal fluxes is the most important property of this discretization from the users perspective. It will be proven that under certain assumptions on the triangulation the particle density remains positive in the iterative solution algorithm. Connected to this result an a priori error estimate for the discrete solution of linear convection-diffusion equations is derived. The local charge transport phenomena will be resolved by an adaptive algorithm, which is based on a posteriori error estimators. At that stage a comparison of different estimations is performed. Additionally a method to effectively estimate the error in local quantities derived from the solution, so-called "functional outputs", is developed by transferring the dual weighted residual method to mixed finite elements. For a model problem we present how this method can deliver promising results even when standard error estimator fail completely to reduce the error in an iterative mesh refinement process.

Implementation of monotonic higher order upwind scheme in KIVA 4

KIVA is a FORTRAN code developed by Los Alamos national lab to simulate complete engine cycle. KIVA is a flow solver code which is used to perform calculation of properties in a fluid flow field. It involves using various numerical schemes and methods to solve the Navier-Stokes equation. This project involves improving the accuracy of one such scheme by upgrading it to a higher order scheme. The numerical scheme to be modified is used in the critical final stage calculation called as rezoning phase. The primitive objective of this project is to implement a higher order numerical scheme, to validate and verify that the new scheme is better than the existing scheme. The latest version of the KIVA family (KIVA 4) is used for implementing the higher order scheme to support handling the unstructured mesh. The code is validated using the traditional shock tube problem and the results are verified to be more accurate than the existing schemes in reference with the analytical result. The convection test is performed to compare the computational accuracy on convective transfer; it is found that the new scheme has less numerical diffusion compared to the existing schemes. A four valve pentroof engine, an example case of KIVA package is used as application to ensure the stability of the scheme in practical application. The results are compared for the temperature profile. In spite of all the positive results, the numerical scheme implemented has a downside of consuming more CPU time for the computational analysis. The detailed comparison is provided. However, in an overview, the implementation of the higher order scheme in the latest code KIVA 4 is verified to be successful and it gives better results than the existing scheme which satisfies the objective of this project.

Maximum principle preserving high order schemes for convection-dominated diffusion equations

The maximum principle is an important property of solutions to PDE. Correspondingly, it's of great interest for people to design a high order numerical scheme solving PDE with this property maintained. In this thesis, our particular interest is solving convection-dominated diffusion equation. We first review a nonconventional maximum principle preserving(MPP) high order finite volume(FV) WENO scheme, and then propose a new parametrized MPP high order finite difference(FD) WENO framework, which is generalized from the one solving hyperbolic conservation laws. A formal analysis is presented to show that a third order finite difference scheme with this parametrized MPP flux limiters maintains the third order accuracy without extra CFL constraint when the low order monotone flux is chosen appropriately. Numerical tests in both one and two dimensional cases are performed on the simulation of the incompressible Navier-Stokes equations in vorticity stream-function formulation and several other problems to show the effectiveness of the proposed method.

Toward assessing the effects of aerosols on deep convection: a numerical study using the WRF-Chemistry model

As the formative agents of cloud droplets, aerosols play an undeniably important role in the development of clouds and precipitation. Few meteorological models have been developed or adapted to simulate aerosols and their contribution to cloud and precipitation processes. The Weather Research and Forecasting model (WRF) has recently been coupled with an atmospheric chemistry suite and is jointly referred to as WRF-Chem, allowing atmospheric chemistry and meteorology to influence each other’s evolution within a mesoscale modeling framework. Provided that the model physics are robust, this framework allows the feedbacks between aerosol chemistry, cloud physics, and dynamics to be investigated. This study focuses on the effects of aerosols on meteorology, specifically, the interaction of aerosol chemical species with microphysical processes represented within the framework of the WRF-Chem. Aerosols are represented by eight size bins using the Model for Simulating Aerosol Interactions and Chemistry (MOSAIC) sectional parameterization, which is linked to the Purdue Lin bulk microphysics scheme. The aim of this study is to examine the sensitivity of deep convective precipitation modeled by the 2D WRF-Chem to varying aerosol number concentration and aerosol type. A systematic study has been performed regarding the effects of aerosols on parameters such as total precipitation, updraft/downdraft speed, distribution of hydrometeor species, and organizational features, within idealized maritime and continental thermodynamic environments. Initial results were obtained using WRFv3.0.1, and a second series of tests were run using WRFv3.2 after several changes to the activation, autoconversion, and Lin et al. microphysics schemes added by the WRF community, as well as the implementation of prescribed vertical levels by the author. The results of WRFv3.2 runs contrasted starkly with WRFv3.0.1 runs. The WRFv3.0.1 runs produced a propagating system resembling a developing squall line, whereas the WRFv3.2 runs did not. The response of total precipitation, updraft/downdraft speeds, and system organization to increasing aerosol concentrations were opposite between runs with different versions of WRF. Results of the WRFv3.2 runs, however, were in better agreement in timing and magnitude of vertical velocity and hydrometeor content with a WRFv3.0.1 run using single-moment Lin et al. microphysics, than WRFv3.0.1 runs with chemistry. One result consistent throughout all simulations was an inhibition in warm-rain processes due to enhanced aerosol concentrations, which resulted in a delay of precipitation onset that ranged from 2-3 minutes in WRFv3.2 runs, and up to 15 minutes in WRFv.3.0.1 runs. This result was not observed in a previous study by Ntelekos et al. (2009) using the WRF-Chem, perhaps due to their use of coarser horizontal and vertical resolution within their experiment. The changes to microphysical processes such as activation and autoconversion from WRFv3.0.1 to WRFv3.2, along with changes in the packing of vertical levels, had more impact than the varying aerosol concentrations even though the range of aerosol tested was greater than that observed in field studies. In order to take full advantage of the input of aerosols now offered by the chemistry module in WRF, the author recommends that a fully double-moment microphysics scheme be linked, rather than the limited double-moment Lin et al. scheme that currently exists. With this modification, the WRF-Chem will be a powerful tool for studying aerosol-cloud interactions and allow comparison of results with other studies using more modern and complex microphysical parameterizations.